Lifted Inference for Relational Hybrid Models

Probabilistic Graphical Models (PGMs) promise to play a prominent role in many complex real-world systems. Probabilistic Relational Graphical Models (PRGMs) scale the representation and learning of PGMs. Answering questions using PRGMs enables many current and future applications, such as medical informatics, environmental engineering, financial forecasting and robot localizations. Scaling inference algorithms for large models is a key challenge for scaling up current applications and enabling future ones. This thesis presents new insights into large-scale probabilistic graphical models. It provides fresh ideas for maintaining a compact structure when answering questions or inferences about large, continuous models. The insights result in a key contribution, the Lifted Relational Kalman filter (LRKF), an efficient estimation algorithm for large-scale linear dynamic systems. It shows that the new relational Kalman filter enables scaling the exact vanilla Kalman filter from 1,000 to 1,000,000,000 variables. Another key contribution of this thesis is that it proves that typically used probabilistic first-order languages, including Markov Logic Networks (MLNs) and First-Order Probabilistic Models (FOPMs), can be reduced to compact probabilistic graphical representations under reasonable conditions. Specifically, this thesis shows that aggregate operators and the existential quantification in the languages are accurately approximated by linear constraints in the Gaussian distribution. In general, probabilistic first-order languages are transformed into nonparametric variational models where lifted inference algorithms can efficiently solve inference problems.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Computer Science

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2012

Author dc:creator

• Choi, Jaesik

Contributors dc:contributor

• Amir, Eyal
• Roth, Dan
• LaValle, Steven M.
• Poole, David

• Probabilistic Graphical Models
• Relational Hybrid Models
• Lifted Inference
• First-Order Probabilistic Models
• Probabilistic Logic
• Kalman filter
• Relational Kalman filter
• Variational Learning, Markov Logic Networks

Statement dc:rights

• Copyright 2012 Jaesik Choi

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/32004

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/32004